{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MRYJX4KSVSAACNCJEE3KU3BTI3","short_pith_number":"pith:MRYJX4KS","canonical_record":{"source":{"id":"1710.05660","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-10-12T12:19:01Z","cross_cats_sorted":[],"title_canon_sha256":"235b5d70e0a69ca6c8f11cb0c42e53021b481b6f5be3045abb125d41f5d722b6","abstract_canon_sha256":"46d4f5e3fa94c7b086a5a76c674bcd7258acd4a51406d23e9ab03f412e583d1d"},"schema_version":"1.0"},"canonical_sha256":"64709bf152ac800134492136aa6c3346d8909ddeeb86056279ea733fddf714fa","source":{"kind":"arxiv","id":"1710.05660","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05660","created_at":"2026-05-18T00:32:48Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05660v1","created_at":"2026-05-18T00:32:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05660","created_at":"2026-05-18T00:32:48Z"},{"alias_kind":"pith_short_12","alias_value":"MRYJX4KSVSAA","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MRYJX4KSVSAACNCJ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MRYJX4KS","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MRYJX4KSVSAACNCJEE3KU3BTI3","target":"record","payload":{"canonical_record":{"source":{"id":"1710.05660","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-10-12T12:19:01Z","cross_cats_sorted":[],"title_canon_sha256":"235b5d70e0a69ca6c8f11cb0c42e53021b481b6f5be3045abb125d41f5d722b6","abstract_canon_sha256":"46d4f5e3fa94c7b086a5a76c674bcd7258acd4a51406d23e9ab03f412e583d1d"},"schema_version":"1.0"},"canonical_sha256":"64709bf152ac800134492136aa6c3346d8909ddeeb86056279ea733fddf714fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:48.623648Z","signature_b64":"yOPwHrgfvsThzGq0i9rITMxFegnZD1lfjF0gY9448rYJURllS9SJHNH5eHcwPRfI806GAIYFKn7ROBveW4KIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64709bf152ac800134492136aa6c3346d8909ddeeb86056279ea733fddf714fa","last_reissued_at":"2026-05-18T00:32:48.622816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:48.622816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.05660","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tOkhovfXi9SVcWOOIy1CWXnrZ+f4mGwqBNl5q4P7lp7ozwOYa+B3TqQMM2CHmkay+bj5mCvPHzGtcqeFR1jKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:08:10.766524Z"},"content_sha256":"2246dd0b7a6ce2a0f3882ed6d7f43b42bfcfe559f6631fa2482463999473fe99","schema_version":"1.0","event_id":"sha256:2246dd0b7a6ce2a0f3882ed6d7f43b42bfcfe559f6631fa2482463999473fe99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MRYJX4KSVSAACNCJEE3KU3BTI3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantitative Graph Theory: A new branch of graph theory and in network science","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SI","authors_text":"Frank Emmert-Streib, Matthias Dehmer, Yongtang Shi","submitted_at":"2017-10-12T12:19:01Z","abstract_excerpt":"In this paper, we describe {\\sc quantitative graph theory} and argue it is a new graph-theoretical branch in network science, however, with significant different features compared to classical graph theory. The main goal of quantitative graph theory is the structural quantification of information contained in complex networks by employing a {\\it measurement approach} based on numerical invariants and comparisons. Furthermore, the methods as well as the networks do not need to be deterministic but can be statistic. As such this complements the field of classical graph theory, which is descripti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05660","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vh/7lunchtf8l+Upsuj1F0vmLz2S6NXLK159Wo33ZZX+cRr5L0AUyR2gHHS2ayfGg/nf05sPkNR6pR5O4bbBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:08:10.767162Z"},"content_sha256":"eaea0ee4fbf55f51f92a769e73d36f8e4acd44132d04cda795072283cdacb2dc","schema_version":"1.0","event_id":"sha256:eaea0ee4fbf55f51f92a769e73d36f8e4acd44132d04cda795072283cdacb2dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MRYJX4KSVSAACNCJEE3KU3BTI3/bundle.json","state_url":"https://pith.science/pith/MRYJX4KSVSAACNCJEE3KU3BTI3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MRYJX4KSVSAACNCJEE3KU3BTI3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T00:08:10Z","links":{"resolver":"https://pith.science/pith/MRYJX4KSVSAACNCJEE3KU3BTI3","bundle":"https://pith.science/pith/MRYJX4KSVSAACNCJEE3KU3BTI3/bundle.json","state":"https://pith.science/pith/MRYJX4KSVSAACNCJEE3KU3BTI3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MRYJX4KSVSAACNCJEE3KU3BTI3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MRYJX4KSVSAACNCJEE3KU3BTI3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"46d4f5e3fa94c7b086a5a76c674bcd7258acd4a51406d23e9ab03f412e583d1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-10-12T12:19:01Z","title_canon_sha256":"235b5d70e0a69ca6c8f11cb0c42e53021b481b6f5be3045abb125d41f5d722b6"},"schema_version":"1.0","source":{"id":"1710.05660","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05660","created_at":"2026-05-18T00:32:48Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05660v1","created_at":"2026-05-18T00:32:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05660","created_at":"2026-05-18T00:32:48Z"},{"alias_kind":"pith_short_12","alias_value":"MRYJX4KSVSAA","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MRYJX4KSVSAACNCJ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MRYJX4KS","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:eaea0ee4fbf55f51f92a769e73d36f8e4acd44132d04cda795072283cdacb2dc","target":"graph","created_at":"2026-05-18T00:32:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we describe {\\sc quantitative graph theory} and argue it is a new graph-theoretical branch in network science, however, with significant different features compared to classical graph theory. The main goal of quantitative graph theory is the structural quantification of information contained in complex networks by employing a {\\it measurement approach} based on numerical invariants and comparisons. Furthermore, the methods as well as the networks do not need to be deterministic but can be statistic. As such this complements the field of classical graph theory, which is descripti","authors_text":"Frank Emmert-Streib, Matthias Dehmer, Yongtang Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-10-12T12:19:01Z","title":"Quantitative Graph Theory: A new branch of graph theory and in network science"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05660","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2246dd0b7a6ce2a0f3882ed6d7f43b42bfcfe559f6631fa2482463999473fe99","target":"record","created_at":"2026-05-18T00:32:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"46d4f5e3fa94c7b086a5a76c674bcd7258acd4a51406d23e9ab03f412e583d1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2017-10-12T12:19:01Z","title_canon_sha256":"235b5d70e0a69ca6c8f11cb0c42e53021b481b6f5be3045abb125d41f5d722b6"},"schema_version":"1.0","source":{"id":"1710.05660","kind":"arxiv","version":1}},"canonical_sha256":"64709bf152ac800134492136aa6c3346d8909ddeeb86056279ea733fddf714fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64709bf152ac800134492136aa6c3346d8909ddeeb86056279ea733fddf714fa","first_computed_at":"2026-05-18T00:32:48.622816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:48.622816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yOPwHrgfvsThzGq0i9rITMxFegnZD1lfjF0gY9448rYJURllS9SJHNH5eHcwPRfI806GAIYFKn7ROBveW4KIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:48.623648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.05660","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2246dd0b7a6ce2a0f3882ed6d7f43b42bfcfe559f6631fa2482463999473fe99","sha256:eaea0ee4fbf55f51f92a769e73d36f8e4acd44132d04cda795072283cdacb2dc"],"state_sha256":"6371da7764315ecb8b87eeada43931d098385e416c2ee973bce28280bdcc6baa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2lAo6z30jN21p2rT7IaQqTElf5DXoXVLJVnZGtTkIKpIYfPO29Ou9/bkBSU7y8fhaPNXS5DSXbebzMzNMevBDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:08:10.770631Z","bundle_sha256":"bdc09e15a29bffc034fe4459ed328e6f97587daaec17c187de9605d19be040b5"}}